Question

. A monopolist faces two types of consumers: low demand consumers and high demand consumers. A high demand consumer has valuation equal to VH(q) = 10 + q - q 2 for q units of output and a low demand consumer has valuation equal to VL(q) = 10 + q - 2q2 for q units of output. There are equal numbers of each type of consumer. Marginal cost of production is constant and equal to c. The monopolist wishes to offer two packages (qL,RL) and (qH,RH) where qi is the quantity of output in package i and Ri is the total price for package i.

a. Assuming the monopolist can observe the type of any given consumer, set up the monopolist’s profit function with relevant constraints and solve this function for the profit maximizing quantities and total package prices (qL,RL) and (qH,RH) .(Again, insert your functions for V from the start.)

b. Assuming the monopolist cannot observe the type of any given consumer, set up and solve monopolist’s profit function with relevant constraints.

Answer 1

The following problem relates to a monopolist who faces two types of consumers. The first type prefers a high quality product and the other type prefers to compromise with a low quality product. The first one is categorised as a High Type (H) and the other as a Low Type (L).

a.

For the High Type (H)

Relevant constraint is q=q_H + q_L

For Low Type (L)

b.

Let the probability of H type be 'a' and of L type be 'b';

where 0<a,b<1.

The relevant constraint remains the same as in part (a).

Hence, the aforesaid expressions represent the package price in a generalised form.